but on this example, you've not taken into account the fact that [2,3] wins a jackpot and wins a minor prize
as does [1,2]
No --- they don't. Doing so was a mistake in the first example. I said.
If I have tickets [1,2] [2,3]
and the winning ticket is drawn as [2,3] then my first ticket will win a minor prize and my second ticket will win a jackpot prize.....equally if [1,2] is drawn my first ticket will win a jackpot prize, and my second ticket will win a minor prize.....
unless you introduce extra rules about not being able to win both a minor and jackpot prize - which we haven't....
so there's no difference in E(v) between [1,2] [2,3] and [1,2][3,4] they both give me 2a + 16b over 15 rounds....
to plug in some numbers, say jackpot prize (a) was £100 and minor prize (b) was £20
then with tickets [1,2] [2,3] over 15 rounds i'd have an E(v) of....
One jackpot (2/15) : {1,2} {2,3}
Two jackpots (0/15)
One minor prize (8/15) : {1,4} {1,5} {1,6} {3,4} {3,5} {3,6} {1,2} {2,3}
Two minor prizes (4/15) : {2,4} {2,5} {2,6} {1,3}
Lose: (3/15) : {4,5} {4,6} {5,6}
2x100 + 8x20 + 4x40 = £520
and with the tickets [1,2] [3,4] over 15 rounds i'd have an E(v) of.....
One jackpot (2/15) : {1,2} {3,4}
Two jackpots (0/15)
One minor prize (8/15) : {1,5} {1,6} {2,5} {2,6} {3,5} {3,6} {4,5} {4,6}
Two minor prizes (4/15) : {1,4} {1,3} {2,3} {2,4}
Lose (1/15) : {5,6}
2x100 + 8x20+ 4x40 = £520
edit.
ok i think i realise why were talking at cross purposes - i'm assuming that in the example, the minor prizes are fixed amounts, and you're taking them as determined relative to the whole prize fund.....
i've looked up the national lottery breakdown, and whilst 3 numbers are fixed, 4,5,6 are percentages.....
3 numbers £10 1: 57
4 numbers 22% of remaining fund 1: 1,033
5 numbers 10% of remaining fund 1: 55,492
5 numbers and bonus ball 16% of remaining fund 1: 2,330,636
6 numbers 52% of remaining fund 1: 13,983,816
